Optimization Problems

Flashcards covering key optimization concepts and examples from the lecture notes.

In optimization problems, the first step is to read the given information carefully and identify what is known and what needs to be __.

found

Step 3 in the optimization strategy involves assigning a label to the quantity that needs to be or and expressing that quantity as a function of one variable.

maximized, minimized

To find the absolute minimum or maximum of a function f, you should evaluate it at the critical points and the __ of the domain.

endpoints

According to the optimization problem involving the box volume, the only critical point in the domain was __.

3

In Example 2, the quantity to maximize is represented by the function A = __, where w and h are dimensions of the rectangle.

wh

The maximum possible area for the inscribed rectangle in a semicircle occurs when the dimensions satisfy the condition 0 ≤ w ≤ __.

r

To minimize the amount of metal used for the half-liter can, the dimensions must be derived from the relationship between radius r and height h and the area function A = __.

2πr² + 2πrh

In business context, the profit P(x) realized by selling x units is related to the cost C(x) and the revenue R(x) by the formula P(x) = __.

R(x) - C(x)